An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model
Jianping Zhao, Rui Chen, Haiyan Su
Abstract
In this paper, we present an efficient energy stable finite element method for the two phase incompressible Magnetohydrodynamic (MHD) flow which is governed by the incompressible MHD equations and the Cahn-Hilliard equation. The strong nonlinear system governs the dynamics and the coupling of multiple physical fields which are, respectively, the velocity $\mathbf{u}$, the pressure $p$, the magnetic induction $\mathbf{B}$, the concentration $\phi$, and the chemical potential $\mu$. To solve the problem efficiently, we propose a linearized finite element scheme which is absolutely stable in time. Several numerical experiments are shown for demonstrating the competitive behavior of the method.
Topics & Concepts
Magnetohydrodynamic driveFinite element methodCompressibilityMechanicsCahn–Hilliard equationMaterials sciencePhysicsThermodynamicsMagnetohydrodynamicsMathematical analysisMathematicsPlasmaPartial differential equationQuantum mechanicsAdvanced Numerical Methods in Computational MathematicsSolidification and crystal growth phenomenaDifferential Equations and Numerical Methods